// WARNING: Do not change or delete this file! If you do, Perseus might become
// unable to parse the current data format, which will break clients.
// If you need to add more regression tests, add a new file to this directory.
export default {
    answerArea: {
        calculator: false,
        options: {
            content: "",
            images: {},
            widgets: {},
        },
        type: "multiple",
    },
    hints: [
        {
            content:
                "First, since this triangle is equilateral, the triangles on the right and left are congruent, so we can label some other measures with variables:\n\n![](https://ka-perseus-graphie.s3.amazonaws.com/6b0c27f7b0e3b583f30e8fbc0dfa4e685a3c583c.png)",
            images: {
                "https://ka-perseus-graphie.s3.amazonaws.com/6b0c27f7b0e3b583f30e8fbc0dfa4e685a3c583c.png":
                    {
                        height: 288,
                        width: 288,
                    },
            },
            widgets: {},
        },
        {
            content:
                "Since the bisected side is $6$ and it's being cut in half, we have: \n\n$2 \\purple{b} = 6$\n\n$\\purple{b} = 3$",
            images: {},
            widgets: {},
        },
        {
            content:
                "Since the angles of a triangle add up to $\\pi$ radians, we can see that:\n\n$3\\pink{\\varphi} = \\pi$\n\n$\\pink{\\varphi} = \\dfrac{\\pi}{3}$",
            images: {},
            widgets: {},
        },
        {
            content:
                "And since $\\pink{\\varphi} = 2\\blue{\\theta}$,\n\n$\\blue\\theta = \\dfrac{\\pi}{6}$",
            images: {},
            widgets: {},
        },
        {
            content:
                "Finally, let's find $\\red{a}$. We can use the right triangle:\n\n$\\begin{align} \\red{a}^2+ \\purple{b}^2 &= 6^2 \\\\\n\\red{a}^2 + \\purple{\\left(3\\right)}^2 &= 36 \\\\\n\\red{a}^2 &=27 \\\\\n\\red{a} &= \\pm \\sqrt{27} \\\\\n&= 3\\sqrt{3}\n\\end{align}$\n\n($\\red{a}$ is positive because it's a length.)",
            images: {},
            widgets: {},
        },
        {
            content:
                "The sine of an angle in a right triangle is the ratio of the opposite leg to the hypotenuse. In the left right triangle, the side opposite $\\theta$ is $3$ and the hypotenuse is $6$, so:\n\n$\\begin{align}\\sin (\\blue{\\theta})&=\\dfrac{3}{6}\\\\ &= \\frac{1}{2}\\end{align}$",
            images: {},
            widgets: {},
        },
        {
            content:
                "To sum up:\n\n- $\\purple{b} = 3$\n\n\n- $\\red{a} = 3 \\sqrt 3$\n\n\n- $\\blue{\\theta} = \\dfrac{\\pi}{6}$\n\n\n- $\\sin (\\blue{\\theta}) =\\dfrac{1}{2}$\n",
            images: {},
            widgets: {},
        },
    ],
    itemDataVersion: {
        major: 0,
        minor: 1,
    },
    question: {
        content:
            "The following drawing contains an equilateral triangle whose side is $6$ units.  \n$a$ is perpendicular to one of the sides of the triangle.\n\n**Find the values of the following expressions. Don't round. Angle measures should be given in *radians*.**\n\n$\\qquad\\purple{b} = $ [[☃ expression 2]]\n\n$\\qquad\\red{a} = $ [[☃ expression 1]]\n\n$\\qquad\\blue{\\theta} =$ [[☃ expression 3]]\n\n$\\qquad\\sin(\\blue{\\theta}) = $ [[☃ expression 4]]\n\n$\\qquad$![](https://ka-perseus-graphie.s3.amazonaws.com/bee05e004428ab4fb0d8af9c5ca0fe67bc991312.png)\n",
        images: {
            "https://ka-perseus-graphie.s3.amazonaws.com/bee05e004428ab4fb0d8af9c5ca0fe67bc991312.png":
                {
                    height: 288,
                    width: 288,
                },
        },
        widgets: {
            "expression 1": {
                graded: true,
                options: {
                    answerForms: [
                        {
                            considered: "correct",
                            form: false,
                            simplify: false,
                            value: "sqrt(3)*3",
                        },
                    ],
                    buttonSets: ["basic", "prealgebra"],
                    functions: ["f", "g", "h"],
                    times: false,
                },
                type: "expression",
                version: {
                    major: 1,
                    minor: 0,
                },
            },
            "expression 2": {
                graded: true,
                options: {
                    answerForms: [
                        {
                            considered: "correct",
                            value: "3",
                        },
                    ],
                    buttonSets: ["basic", "prealgebra"],
                    functions: ["f", "g", "h"],
                    times: false,
                },
                type: "expression",
                version: {
                    major: 1,
                    minor: 0,
                },
            },
            "expression 3": {
                graded: true,
                options: {
                    answerForms: [
                        {
                            considered: "correct",
                            form: false,
                            simplify: false,
                            value: "pi/6",
                        },
                    ],
                    buttonSets: ["basic", "prealgebra"],
                    functions: ["f", "g", "h"],
                    times: false,
                },
                type: "expression",
                version: {
                    major: 1,
                    minor: 0,
                },
            },
            "expression 4": {
                graded: true,
                options: {
                    answerForms: [
                        {
                            considered: "wrong",
                            form: true,
                            key: "1",
                            simplify: false,
                            value: "\\sin\\left(\\frac{\\pi}{6}\\right)",
                        },
                        {
                            considered: "correct",
                            form: false,
                            key: null,
                            simplify: false,
                            value: "1/2",
                        },
                    ],
                    buttonSets: ["basic", "prealgebra"],
                    functions: ["f", "g", "h"],
                    times: false,
                },
                type: "expression",
                version: {
                    major: 1,
                    minor: 0,
                },
            },
        },
    },
};
